diff --git a/candle-nn/tests/layer_norm.rs b/candle-nn/tests/layer_norm.rs
new file mode 100644
index 00000000..e4b962b4
--- /dev/null
+++ b/candle-nn/tests/layer_norm.rs
@@ -0,0 +1,43 @@
+#[cfg(feature = "mkl")]
+extern crate intel_mkl_src;
+
+use anyhow::Result;
+use candle::{Device, Tensor};
+use candle_nn::LayerNorm;
+
+#[test]
+fn layer_norm() -> Result<()> {
+    let device = &Device::Cpu;
+    let w = Tensor::new(&[3f32], device)?;
+    let b = Tensor::new(&[0.5f32], device)?;
+    let ln = LayerNorm::new(w, b, 1e-8);
+
+    let two = Tensor::new(&[[[2f32]]], device)?;
+    let res = ln.forward(&two)?.flatten_all()?;
+    assert_eq!(res.to_vec1::<f32>()?, [0.5f32]);
+
+    let inp = Tensor::new(&[[[4f32, 0f32]]], device)?;
+    let res = ln.forward(&inp)?;
+    assert_eq!(res.to_vec3::<f32>()?, [[[3.5f32, -2.5]]]);
+
+    let inp = Tensor::new(&[[[1f32, 2., 3.], [4., 5., 6.], [9., 8., 7.]]], device)?;
+    let res = ln.forward(&inp)?;
+    assert_eq!(
+        res.to_vec3::<f32>()?,
+        [[
+            [-3.1742344, 0.5, 4.1742344],
+            [-3.1742344, 0.5, 4.1742344],
+            [4.1742344, 0.5, -3.1742344]
+        ]]
+    );
+    let mean = (res.sum(&[2])? / 3.0)?;
+    // The average value should be `b`.
+    assert_eq!(mean.to_vec3::<f32>()?, [[[0.5], [0.5], [0.5]]]);
+    let std = (res.broadcast_sub(&mean)?.sqr()?.sum(&[2])?.sqrt()? / 3.0)?;
+    // The standard deviation should be sqrt(`w`).
+    assert_eq!(
+        std.to_vec3::<f32>()?,
+        [[[1.7320508], [1.7320508], [1.7320508]]]
+    );
+    Ok(())
+}